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The Paradox 
of Identity


Call a semantics for singular terms extensionalist if it embraces (1) and classical if it embraces (2).
  1. The meaning of a singular term is exhausted by its reference.
  2. The reference of a singular term is an entity that is logically simple.
Call a semantics adequate if it distinguishes material identity (the identity of a and b) and formal identity (the identity of a and a).

Frege reacts to the inadequacy of classical extensionalist semantics by rejecting (1).  This he does without a sideways glance at (2), whose background ontology he implicitly accepts.

In contrast, my account of the difference between material and formal identity replaces that background ontology, the so-called ontology of individuals (van Heijenoort's term), with an ontology whose ground-level objects are ontologically differentiated and logically complex.  The semantics I urge for singular terms, while extensionalist* in the sense of (1), is thus a non-classical semantics in which singular terms take structured individuals, or complexes (as I will say), as their referents.  For, unlike the logically simple units of the ontology of individuals, complexes keep (true) 'a = b' and 'a = a' apart.

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Copyright© 1999, William J. Greenberg, all rights reserved.